Quadratic Equation Formula Explained, With Examples
Every quadratic equation result comes from one formula. Once you understand what goes into it, you can sanity-check any figure you are given, whether by an employer, a bank, a teacher or another website.
The formula
x = (−b ± √(b² − 4ac)) ÷ 2a.
What each input means
- a: the value you enter in the calculator.
- b: the value you enter in the calculator.
- c: the value you enter in the calculator.
Example
For example, with these inputs:
- a: 1
- b: -5
- c: 6
the calculator returns:
- Roots: x₁ = 3, x₂ = 2
- Discriminant: 1
How the result changes
The table keeps the other inputs at their example values and changes a.
| a | Roots | Discriminant |
|---|---|---|
| 1 | x₁ = 3, x₂ = 2 | 1 |
| 0.5 | x₁ = 8.6056, x₂ = 1.3944 | 13 |
| 0.75 | x₁ = 5.0972, x₂ = 1.5695 | 7 |
| 1.25 | x = 2 ± 0.8944i (complex roots) | -5 |
| 1.5 | x = 1.6667 ± 1.1055i (complex roots) | -11 |
Why it matters
These calculations come up in school, at work and in daily life, from PSLE and O-Level practice to measuring a room for new flooring. Doing them by hand builds understanding, and a calculator lets you check the answer instantly.
Rounding is a common source of small errors. Keep full precision during intermediate steps and round only the final answer to the number of decimal places or significant figures the question asks for.
In everyday life the same maths shows up in discounts, recipe scaling, renovation measurements and comparing prices per unit. Being comfortable with it saves money and avoids costly measuring mistakes.
These calculations appear throughout the Singapore syllabus, from primary school percentages and fractions to secondary school algebra and geometry. Understanding the formula makes problem sums easier because you can recognise which quantity is missing.
Related calculations
- Perimeter of a Triangle Calculator: Calculates the perimeter of a triangle from the measurements you enter.
- Perimeter of an Ellipse Calculator: Calculates the perimeter of an ellipse from the measurements you enter.
- Arc Length Calculator: Calculates the arc length from the measurements you enter.
- Volume of a Cube Calculator: Calculates the volume of a cube from the measurements you enter.
Use the Quadratic Equation Solver to plug in your own numbers.
Run your own numbers: Quadratic Equation Solver